The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives $18.8$ years; the standard deviation is $3.8$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a gorilla living between $22.6$ and $30.2$ years.
Explanation: $18.8$ $15$ $22.6$ $11.2$ $26.4$ $7.4$ $30.2$ $99.7\%$ $68\%$ $15.85\%$ $15.85\%$ We know the lifespans are normally distributed with an average lifespan of $18.8$ years. We know the standard deviation is $3.8$ years, so one standard deviation below the mean is $15$ years and one standard deviation above the mean is $22.6$ years. Two standard deviations below the mean is $11.2$ years and two standard deviations above the mean is $26.4$ years. Three standard deviations below the mean is $7.4$ years and three standard deviations above the mean is $30.2$ years. We are interested in the probability of a gorilla living between $22.6$ and $30.2$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $99.7\%$ of the gorillas will have lifespans within 3 standard deviations of the average lifespan. It also tells us that $68\%$ of the gorillas will have lifespans within 1 standard deviation of the mean. The probability of a particular gorilla living between $22.6$ and $30.2$ years is $\color{orange}{15.85\%}$.